In a medium bowl, combine graham cracker crumbs and granulated sugar until well mixed. Pour in the melted butter and stir until the mixture resembles wet sand. Press this crust firmly into a greased 9x13 inch pan, ensuring it's evenly distributed. Refrigerate the crust for at least 30 minutes to set while you make the filling.

In a saucepan, whisk together the granulated sugar and cornstarch with cold water over medium heat. Bring this mixture to a gentle boil, stirring constantly until it thickens and becomes translucent, about 3-5 minutes. Once thickened, remove from heat, stir in the peach jello until dissolved, and fold in the sliced fresh peaches. Allow this mixture to cool completely in the refrigerator.

In a large mixing bowl, beat the softened cream cheese with powdered sugar using an electric mixer on medium speed until smooth and creamy, about 2 minutes. Gradually mix in the whipped topping and vanilla extract until fully combined, achieving a light and fluffy texture.

Spread the cream cheese filling evenly over the chilled graham cracker crust, smoothing it out with a spatula. Carefully pour the cooled peach topping over the cream cheese layer, spreading it gently to avoid mixing the two layers. Cover the dessert with plastic wrap and refrigerate for 4-5 hours.

After the cheesecake has set, cut it into squares and serve chilled. Optionally, add dollops of whipped topping on each serving for an extra creamy finish.